A New Numerical Method for Solving Radiation Driven Winds from Hot Stars

We present a general method for solving the non–linear differential equation of monotonically increasing steady–state radiation driven winds. We graphically identify all the singular points before transforming the momentum equation to a system of differential equations with all the gradients explicitly give. This permits a topological classification of all singular points and to calculate the maximum and minimum mass–loss of the wind. We use our method to analyse for the first time the topology of the non–rotating frozen in ionisation m–CAK wind, with the inclusion of the finite disk correction factor and find up to 4 singular points, three of the x–type and one attractor–type. The only singular point (and solution passing through) that satisfies the boundary condition at the stellar surface is the standard m–CAK singular point.